The cross hatched lines are the cables that hold the roof down.
Air supported structures are, as their name states, held up by air pressure. The inside of the structures is pressurized like a balloon. while this might seem at first to be uncomfortable to the occupants of the structure, the pressure differential is no greater than that of ordinary barometric fluctuations. Common uses of air supported structures include sports stadiums, the "bubbles" used to cover tennis courts and pools, and many other temporary shelters.
The two basic types of air supported structures are high profile and low profile. Profile refers to the height to the structure relative to its span. High profile structures are typically used for temporary or storage facilities and are often free standing, which means they have no foundation upon which they rest. Low profile structures are used to span long distances such as sports stadiums, also low profile structures tend to be placed upon a building rather then the ground itself, thus being used as roofs. This is due to the forces involved in supported the structure. High profile air supported structures are less common today because the cost of comparable tension fabric structures has been reduced considerable.
Here are some geometric plans for low profile air supported structures:
The cross hatched lines are the cables that hold the roof down.
First costs for an air-supported roof always have compared favorably with those of conventional roof structures. On a cost-per-seat basis, the advantage is even more evident. The savings come from lower construction and supporting structure costs plus overall economy of design. Architecturally, the design are very elegant and dramatic.
Unintentional deflation and the cost associated with it is the major problem with these structures. The most common cause of deflation is accumulating snow and resulting ponding. The introduction of design refinements, such as computer patterning, and greater knowledge and planning on the part of operators has helped reduce the occurrences in the recent past.
Air pressure is used to support and stabilize air supported structures. When air is placed under pressure it exerts a uniform force in all directions. This force is used to support the fabric. The cables do not support the fabric, but hold it down. The fabric is attached to the cables in panels resulting in a hybrid membrane. The hybrid membrane transfers the stresses from the fabric to the cables. The cables are attached to a compression ring, which resists the uplifting forces.
The most basic shape is a low profile oval with a diagonal cable pattern and a funicular compression ring. Funicular implies that there are no bending moments in the compression ring. A rectangular shape with modified corners and two way cable systems will keep a compression ring funicular. One way cable systems in a modified rectangular structure produce moments in the compression ring. High profile air supported structures may use one or two way cable systems or just fabric alone. Consideration of fabric design aand shipping will limit cable spacing to a maximum of 45 ft(14m). Due to fabrication and cost of connections, the minimum cable spacing considered economically fiasible is 35 ft(11m) on center.
There are countless soapbubble shapes, all of which conform to the general condition of stress uniformity. This number can still be increased if stress differrenernces are admitted (fig. 1). Nevertheless, only a fraction of all the imaginable shapes can be formed pneumatically.Pneumatic shapes are characterized by double- curvature surfaces. Saddle- shaped and single- curvature surfaces are less frequently formed thatn spherical surfaces. Plane surfaces are impossible in actual practice.  It is obvious that a membrane, shaped as shown by the dotted lines will be forced outward as soon as internal pressure is applied, The shape by the dooted lines can- not, therefore, be formed pneumatically.If we have a semicylinder made of pliable but inelastic skin and having a flat top (left lowwer fig.)and we apply internal pressure to it, the top will bulge outward (fig. 4), and pleats will appear. The top of the cylinder becomes a surface of revolution, with zero circumferential stresses in the region of the pleats. A pneumatic skin can be shaped like a flattened ball (fig. 6) deviating only slightly from a sphere. In a body of revolution (fig. 5), the membrane is not stressed in a tangential direction (parallel of latitude) if the radius of curvature is wqual to half the distance P-N (on fig. 5 upper right). If the radius of curvature becomes smaller - pleats will appear. If such a body of revolution is formed, it will be noted that even with low elasticity of deformability of the skin, 
(fig. 4) |
  the shape has a tendency to become spherical. The reason for this is that the radial stresses at the apex of such a body are theoretically infinite.It is therefore possible to form a certain shape pneumatically if a body of revolution can be inscribed in it. The surest test, however, is to inscribe spheres. Since a sphere of variable diameter can be moved along an axis (fig. 7), the enveloping surface can be formed pneumatically. With the aid of inscribed spheres it can be ascertained whether different shapes (fig 8 to 13) can be formed pneumatically. The spheres can moved along any curve (fig. 14), provided the radius of curvature of the latter is not too small in relation to the diameter of the sphere. Branches can be constructed on the same manner.  |
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